pith. sign in

arxiv: 2511.08014 · v2 · submitted 2025-11-11 · ⚛️ physics.flu-dyn

A Comprehensive Regime Diagram of Dynamical Modes of Triple Flickering Buoyant Diffusion Flames: Experimental and Model Investigations

Hanxu Wang , Tao Yang , Yicheng Chi , Zhenyu Zhang , Peng Zhang This is my paper

Pith reviewed 2026-05-18 00:03 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn
keywords triple flickering flamesbuoyant diffusion flamesdynamical modesregime diagramStuart-Landau oscillatortime-delay couplingsynchronizationbifurcation
0
0 comments X

The pith

Moving one flame continuously maps out synchronization modes among three flickering buoyant flames.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The study examines three flickering laminar buoyant diffusion flames placed in an isosceles triangle to understand how they couple and synchronize. By moving the vertex flame at controlled speeds while independently changing the base length and fuel flow rate, the authors bypass the constraints of fixed discrete positions and generate a dense map of observed behaviors. This produces a regime diagram that classifies the dynamical modes and identifies three previously unreported modes. A model treating each flame as a Stuart-Landau oscillator with time-delay coupling reproduces the experimental patterns and links them to bifurcations in the coupled system. The work matters for anyone designing or analyzing arrays of flames, because the same coupling mechanisms appear in larger burners and can influence stability.

Core claim

Based on experimental observations, a comprehensive regime diagram was established to classify the dynamical modes of triple flickering buoyant diffusion flames. Notably, three previously unreported dynamical modes were identified for the first time. A Stuart-Landau oscillator model with time-delay coupling was employed, which successfully reproduces the experimentally observed dynamical modes. Experimentally observed dynamical modes reveal a bifurcation diagram for the coupled triple Stuart-Landau system.

What carries the argument

Stuart-Landau oscillator model with time-delay coupling, used to represent each flame's flickering amplitude and phase with delays that encode interaction times between the three flames.

If this is right

  • The regime diagram organizes observed modes according to triangle size, fuel flow rate, and vertex movement velocity.
  • Three new dynamical modes expand the catalog of possible synchronization states in triple flame systems.
  • The time-delay Stuart-Landau model reproduces the transitions between modes without solving the full fluid equations.
  • The experimental modes correspond directly to bifurcations in the coupled triple Stuart-Landau system.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The continuous-variation technique could be applied to other multi-flame geometries to discover additional modes without exhaustive static testing.
  • If the delayed-oscillator model scales, it offers a low-cost way to forecast stability limits in larger flame arrays used in industrial burners.
  • The same coupling framework might describe interactions in non-flame oscillator systems, such as groups of vortex wakes or acoustic resonators.

Load-bearing premise

That continuously moving the vertex flame at controlled speed produces dynamical modes equivalent to those found in static fixed-position configurations at matching effective parameters.

What would settle it

Performing a separate set of experiments with the three flames held completely fixed at discrete positions corresponding to the same L and Q values and checking whether the same sequence of modes appears as the vertex flame is stepped through those positions.

Figures

Figures reproduced from arXiv: 2511.08014 by Hanxu Wang, Peng Zhang, Tao Yang, Yicheng Chi, Zhenyu Zhang.

Figure 7
Figure 7. Figure 7: Phase trajectories of six typical dynamical modes in the triple flame system from [PITH_FULL_IMAGE:figures/full_fig_p017_7.png] view at source ↗
Figure 12
Figure 12. Figure 12: Mode IV-2: asymmetric partially in-phase mode reproduced by the Stuart￾Landau model. (a) Phase difference of three S-L oscillators (𝐾 = 0.25 , 𝜏1 = 2.20 , 𝜏2 = 3.40). (b) All model parameters of 𝐾, 𝜏1, and 𝜏2 for Mode IV-2 in the ranges of −0.5 < 𝐾 < 0.5 and 0 < 𝜏1, 𝜏2 < 5 [PITH_FULL_IMAGE:figures/full_fig_p021_12.png] view at source ↗
read the original abstract

The triple-flame system serves as the fundamental unit for understanding multi-flame interactions, revealing critical coupling mechanisms that scale to complex burner arrays. In this study, we investigated triple flame oscillators, consisting of three flickering laminar buoyant diffusion flames arranged in an isosceles triangular configuration, to construct a comparative regime diagram of dynamical modes. To overcome the limited experimental observability caused by the discretization of geometric parameters, we enabled continuous motion of the vertex flame at a controlled speed V, while independently varying the base length L and the fuel flow rate Q. We conducted a systematic investigation of the triple flame coupling behaviors by varying the triangle size, fuel flow rate, and vertex flame movement velocity. Based on the experimental observations, a comprehensive regime diagram was established to classify the dynamical modes of triple flickering buoyant diffusion flames. Notably, three previously unreported dynamical modes were identified for the first time. To interpret these complex flame interactions, a Stuart-Landau oscillator model with time-delay coupling was employed, which successfully reproduces the experimentally observed dynamical modes. Experimentally observed dynamical modes reveal a bifurcation diagram for the coupled triple Stuart-Landau system, elucidating the transitions between different synchronization modes.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript reports an experimental study of dynamical modes in three flickering buoyant diffusion flames arranged in an isosceles triangular geometry. By continuously translating the vertex flame at controlled speed V while varying base length L and fuel flow rate Q, the authors construct a regime diagram that classifies observed synchronization states, including three previously unreported modes. A Stuart-Landau oscillator model with time-delay coupling is employed to reproduce the modes and to map the associated bifurcation diagram for the coupled triple-oscillator system.

Significance. If the continuous-sweep method is shown to be dynamically equivalent to static configurations, the work would deliver a valuable comprehensive regime diagram for triple-flame interactions together with a reduced-order model that captures the observed bifurcations. The systematic exploration and identification of new modes constitute a concrete advance for understanding multi-flame coupling. The modeling effort is credited for providing an explicit bifurcation diagram, although its predictive status depends on how the coupling parameters were obtained.

major comments (2)
  1. [Experimental procedure for varying triangle size] The regime diagram and the three new modes rest on continuous variation of L achieved by moving the vertex flame at finite speed V. The manuscript provides no systematic test that the observed synchronization states remain unchanged for sufficiently small V, nor does it report the ratio of the natural flickering period to the time required to traverse one characteristic length at speed V. If this ratio is not ≪ 1, the sweep introduces advective and phase-lag effects absent from static isosceles triangles, rendering the reported boundaries and new modes potentially non-reproducible in fixed-geometry experiments.
  2. [Modeling section] The Stuart-Landau model with time-delay coupling is reported to reproduce the experimentally observed modes and to yield the bifurcation diagram. It is not stated whether the coupling strengths and delays were fixed from independent physical estimates or adjusted to match the target data set. Without this information the reproduction may be post-hoc rather than predictive, weakening the claim that the model elucidates the transitions between synchronization modes.
minor comments (2)
  1. [Abstract] The abstract states that a 'comprehensive regime diagram' was established but does not indicate the explored ranges of L, Q and V or the quantitative criteria used to assign a given trajectory to a particular mode.
  2. [Figures and captions] Figure captions and the regime diagram itself would benefit from explicit indication of the number of independent realizations and any uncertainty in the reported mode boundaries.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive review. The comments have prompted us to clarify key aspects of our experimental and modeling approaches. Below we respond point by point to the major comments.

read point-by-point responses

  1. Referee: [Experimental procedure for varying triangle size] The regime diagram and the three new modes rest on continuous variation of L achieved by moving the vertex flame at finite speed V. The manuscript provides no systematic test that the observed synchronization states remain unchanged for sufficiently small V, nor does it report the ratio of the natural flickering period to the time required to traverse one characteristic length at speed V. If this ratio is not ≪ 1, the sweep introduces advective and phase-lag effects absent from static isosceles triangles, rendering the reported boundaries and new modes potentially non-reproducible in fixed-geometry experiments.

    Authors: We agree that demonstrating the equivalence between the continuous sweep and static configurations is important for the validity of the regime diagram. In the revised manuscript, we have included additional experiments and analysis to address this. Specifically, we selected several representative points in the parameter space and compared the dynamical modes observed during slow continuous sweeps (with V chosen such that the sweep time scale is much longer than the flickering period) to those in fixed static geometries. The modes and transition boundaries were found to be consistent within experimental uncertainty. We have also added the ratio of the natural flickering period to the sweep time, which is approximately 1/20 for the velocities employed, satisfying the condition ≪ 1. These additions are in the Experimental Methods and Results sections. revision: yes

  2. Referee: [Modeling section] The Stuart-Landau model with time-delay coupling is reported to reproduce the experimentally observed modes and to yield the bifurcation diagram. It is not stated whether the coupling strengths and delays were fixed from independent physical estimates or adjusted to match the target data set. Without this information the reproduction may be post-hoc rather than predictive, weakening the claim that the model elucidates the transitions between synchronization modes.

    Authors: We appreciate the referee pointing out the need for clarity on parameter determination. The coupling delays were estimated independently from the time for hydrodynamic perturbations to propagate between the flames, using the measured flow velocities and separations. The coupling strengths were derived from a scaling based on the inverse square of the distance, motivated by the far-field decay of buoyant plume interactions. These values were not fitted to the synchronization data but fixed a priori. In the revised manuscript, we have explicitly described this procedure in the Modeling section and included a brief sensitivity study showing that the bifurcation diagram remains qualitatively unchanged for small variations in these parameters. revision: yes

Circularity Check

1 steps flagged

Stuart-Landau reproduction of modes and bifurcation diagram reduces to parameter fitting on experimental data

specific steps
  1. fitted input called prediction [Abstract]
    "a Stuart-Landau oscillator model with time-delay coupling was employed, which successfully reproduces the experimentally observed dynamical modes. Experimentally observed dynamical modes reveal a bifurcation diagram for the coupled triple Stuart-Landau system"

    The model is presented as successfully reproducing the modes and the observed modes are said to reveal the model's bifurcation diagram. Absent any statement that coupling parameters and delays were determined independently of the target synchronization states, the reproduction and the derived bifurcation diagram are statistically forced by fitting to the same experimental data set.

full rationale

The derivation chain consists of (1) experimental regime diagram obtained via continuous vertex-flame motion at speed V and (2) Stuart-Landau model with time-delay coupling that 'successfully reproduces' the observed modes and whose bifurcation diagram is 'revealed' by those modes. No evidence is given that coupling strengths or delays were fixed from independent measurements or first-principles calculation; the reproduction therefore functions as a post-hoc fit. This matches the 'fitted input called prediction' pattern and raises moderate circularity for the modeling step, while the raw experimental classification itself remains non-circular.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the applicability of the Stuart-Landau oscillator framework to buoyant flame flickering and on the experimental equivalence between continuously moving and static flame configurations. Specific numerical values for coupling coefficients or delays are not given in the abstract and are presumed to be adjusted to match observations.

free parameters (1)
  • coupling strength and time delay parameters
    Likely tuned within the Stuart-Landau model to reproduce the experimentally observed modes, though exact values and fitting procedure are not stated in the abstract.
axioms (1)
  • domain assumption Stuart-Landau oscillator model with time-delay coupling adequately represents the essential dynamics of flickering buoyant diffusion flames
    Invoked to interpret and reproduce the observed synchronization and bifurcation behaviors.

pith-pipeline@v0.9.0 · 5523 in / 1403 out tokens · 86282 ms · 2026-05-18T00:03:12.547987+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

55 extracted references · 55 canonical work pages

  1. [1]

    McManus, T

    K. McManus, T. Poinsot, S.M. Candel, A review of active control of combustion instabilities, Prog. Energy Combust. Sci. 19 (1993) 1-29

    work page 1993

  2. [2]

    Poinsot, Prediction and control of combustion instabilities in real engines, Proc

    T. Poinsot, Prediction and control of combustion instabilities in real engines, Proc. Combust. Inst. 36 (2017) 1-28

    work page 2017

  3. [3]

    Noiray, M

    N. Noiray, M. Bothien, B. Schuermans, Investigation of azimuthal staging concepts in annular gas turbines, Combustion Theory and Modelling 15 (2011) 585-606

    work page 2011

  4. [4]

    Anderson, V

    W.E. Anderson, V. Yang, Liquid rocket engine combustion instability, American Institute of Aeronautics and Astronautics1995

    work page

  5. [5]

    Vignat, D

    G. Vignat, D. Durox, T. Schuller, S. Candel, Combustion dynamics of annular systems, Combust. Sci. Technol. 192 (2020) 1358-1388

    work page 2020

  6. [6]

    Schuller, T

    T. Schuller, T. Poinsot, S. Candel, Dynamics and control of premixed combustion systems based on flame transfer and describing functions, J. Fluid Mech. 894 (2020) P1

    work page 2020

  7. [7]

    Echekki, H

    T. Echekki, H. Kolera-Gokula, A regime diagram for premixed flame kernel-vortex interactions, Phys. Fluids 19 (2007)

    work page 2007

  8. [8]

    A. Fan, S. Minaev, S. Kumar, W. Liu, K. Maruta, Regime diagrams and characteristics of flame patterns in radial microchannels with temperature gradients, Combust. Flame 153 (2008) 479-489

    work page 2008

  9. [9]

    Evans, D.C

    C.J. Evans, D.C. Kyritsis, Operational regimes of rich methane and propane/oxygen flames in mesoscale non-adiabatic ducts, Proc. Combust. Inst. 32 (2009) 3107-3114

    work page 2009

  10. [10]

    Skiba, T.M

    A.W. Skiba, T.M. Wabel, C.D. Carter, S.D. Hammack, J.E. Temme, J.F. Driscoll, Premixed flames subjected to extreme levels of turbulence part I: Flame structure and a new measured regime diagram, Combust. Flame 189 (2018) 407-432

    work page 2018

  11. [11]

    Breer, G

    B. Breer, G. Blanquart, A regime diagram for detonation–turbulence interactions, Proc. Combust. Inst. 41 (2025) 105799

    work page 2025

  12. [12]

    Moreno-Boza, W

    D. Moreno-Boza, W. Coenen, A. Sevilla, J. Carpio, A.L. Sánchez, A. Li?án, Diffusion-flame flickering as a hydrodynamic global mode, Journal of Fluid Mechanics 798 (2016) 997-1014

    work page 2016

  13. [13]

    X. Xia, P. Zhang, A vortex-dynamical scaling theory for flickering buoyant diffusion flames, J. Fluid Mech. 855 (2018) 1156-1169

    work page 2018

  14. [14]

    Thirumalaikumaran, G

    S. Thirumalaikumaran, G. Vadlamudi, S. Basu, Insight into flickering/shedding in buoyant droplet-diffusion flame during interaction with vortex, Combust. Flame 240 (2022) 112002

    work page 2022

  15. [15]

    Balasubramaniyan, N

    M. Balasubramaniyan, N. Gaur, B. Kannan, Soot emissions of steady and oscillatory candle flames, Phys. Fluids 36 (2024)

    work page 2024

  16. [16]

    Legros, T

    G. Legros, T. Gomez, M. Fessard, T. Gouache, T. Ader, P. Guibert, P. Sagaut, J. Torero, Magnetically induced flame flickering, Proc. Combust. Inst. 33 (2011) 1095- 1103

    work page 2011

  17. [17]

    Xiong, S.H

    Y. Xiong, S.H. Chung, M.S. Cha, Instability and electrical response of small laminar coflow diffusion flames under AC electric fields: Toroidal vortex formation and oscillating and spinning flames, Proc. Combust. Inst. 36 (2017) 1621-1628

    work page 2017

  18. [18]

    Forrester, Arrays of coupled chemical oscillators, Sci

    D.M. Forrester, Arrays of coupled chemical oscillators, Sci. Rep. 5 (2015) 1-7

    work page 2015

  19. [19]

    Aravind, I

    M. Aravind, I. Tiwari, V. Vasani, J.-M. Cruz, D.A. Vasquez, P. Parmananda, Ethanol lamp: a simple, tunable flame oscillator and its coupled dynamics, The European Physical Journal Special Topics, (2021) 1-6

    work page 2021

  20. [20]

    Zhang, X

    H. Zhang, X. Xia, Y. Gao, Instability transition of a jet diffusion flame in quiescent environment, Proc. Combust. Inst. 38 (2021) 4971-4978

    work page 2021

  21. [21]

    Bhattacharya, S

    A. Bhattacharya, S. Mondal, S. De, A. Mukhopadhyay, S. Sen, Synchronisation behaviour between two candle flame oscillators with similar and dissimilar amplitudes of oscillations, Combustion Theory and Modelling 27 (2023) 291-316

    work page 2023

  22. [22]

    X. Ju, A. Bunkwang, T. Yamazaki, T. Matsuoka, Y. Nakamura, Flame Flickering can Cease Under Normal Gravity and Atmospheric Pressure in a Horizontally Moving Dual Burner System, Physical Review Applied 19 (2023) 014060

    work page 2023

  23. [23]

    T. Yang, Y. Ma, P. Zhang, Computational identification and Stuart-Landau modeling of collective dynamical behaviors of octuple laminar diffusion flame oscillators, Combustion and Flame 275 (2025)

    work page 2025

  24. [24]

    Okamoto, A

    K. Okamoto, A. Kijima, Y. Umeno, H. Shima, Synchronization in flickering of three-coupled candle flames, Sci. Rep. 6 (2016) 1-10

    work page 2016

  25. [25]

    C. Liu, X. Liu, H. Ge, J. Deng, S. Zhou, X. Wang, F. Cheng, On the influence of distance between two jets on flickering diffusion flames, Combust. Flame 201 (2019) 23-30

    work page 2019

  26. [26]

    Gergely, B

    A. Gergely, B. Sándor, C. Paizs, R. Tötös, Z. Néda, Flickering candle flames and their collective behavior, Sci. Rep. 10 (2020) 1-13

    work page 2020

  27. [27]

    Araya, H

    Y. Araya, H. Ito, H. Kitahata, Bifurcation structure of the flame oscillation, Physical Review E 105 (2022) 044208

    work page 2022

  28. [28]

    T. Yang, Y. Chi, P. Zhang, Vortex interaction in triple flickering buoyant diffusion flames, Proc. Combust. Inst. 39 (2023) 1893-1903

    work page 2023

  29. [29]

    Kitahata, J

    H. Kitahata, J. Taguchi, M. Nagayama, T. Sakurai, Y. Ikura, A. Osa, Y. Sumino, M. Tanaka, E. Yokoyama, H. Miike, Oscillation and synchronization in the combustion of candles, Journal of Physical Chemistry A 113 (2009) 8164-8168

    work page 2009

  30. [30]

    Bunkwang, T

    A. Bunkwang, T. Matsuoka, Y. Nakamura, Similarity of dynamic behavior of buoyant single and twin jet-flame(s), Journal of Thermal Science and Technology 15 (2020) JTST0028-JTST0028

    work page 2020

  31. [31]

    T. Yang, X. Xia, P. Zhang, Vortex-dynamical interpretation of anti-phase and in- phase flickering of dual buoyant diffusion flames, Phys. Rev. Fluids 4 (2019) 053202

    work page 2019

  32. [32]

    T. Yang, X. Xia, P. Zhang, Vortex-dynamical Interpretation of Anti-phase and In- phase Flickering of Dual Buoyant Diffusion Flames, (2018)

    work page 2018

  33. [33]

    Okamoto, A

    K. Okamoto, A. Kijima, Y. Umeno, H. Shima, Synchronization in flickering of three-coupled candle flames, Rep 6 (2016) 36145

    work page 2016

  34. [34]

    Y. Chi, T. Yang, P. Zhang, Dynamical mode recognition of triple flickering buoyant diffusion flames in Wasserstein space, Combust. Flame 248 (2023) 112526

    work page 2023

  35. [35]

    Y. Chi, Z. Hu, T. Yang, P. Zhang, Synchronization modes of triple flickering buoyant diffusion flames: Experimental identification and model interpretation, Physical Review E 109 (2024) 024211

    work page 2024

  36. [36]

    A.E. Biju, S. Srikanth, K. Manoj, S.A. Pawar, R.I. Sujith, Dynamics of minimal networks of limit cycle oscillators, Nonlinear Dynamics, (2024) 1-20

    work page 2024

  37. [37]

    Manoj, S.A

    K. Manoj, S.A. Pawar, R.I. Sujith, Experimental investigation on the susceptibility of minimal networks to a change in topology and number of oscillators, Physical Review E 103 (2021) 022207

    work page 2021

  38. [38]

    T. Chen, X. Guo, J. Jia, J. Xiao, Frequency and phase characteristics of candle flame oscillation, Sci. Rep. 9 (2019) 1-13

    work page 2019

  39. [39]

    L.-D. Chen, J. Seaba, W. Roquemore, L. Goss, Buoyant diffusion flames, Proc. Combust. Inst. 22 (1989) 677-684

    work page 1989

  40. [40]

    Durox, T

    D. Durox, T. Yuan, E. Villermaux, The effect of buoyancy on flickering in diffusion flames, Combust. Sci. Technol. 124 (1997) 277-294

    work page 1997

  41. [41]

    Moreno-Boza, W

    D. Moreno-Boza, W. Coenen, J. Carpio, A.L. Sánchez, F.A. Williams, On the critical conditions for pool-fire puffing, Combust. Flame 192 (2018) 426-438

    work page 2018

  42. [42]

    T. Yang, P. Zhang, Faster flicker of buoyant diffusion flames by weakly rotatory flows, Theor. Comput. Fluid Dyn., (2023) 1-18

    work page 2023

  43. [43]

    Cetegen, T.A

    B.M. Cetegen, T.A. Ahmed, Experiments on the periodic instability of buoyant plumes and pool fires, Combust. Flame 93 (1993) 157-184

    work page 1993

  44. [44]

    H. Sato, K. Amagai, M. Arai, Diffusion flames and their flickering motions related with Froude numbers under various gravity levels, Combust. Flame 123 (2000) 107- 118

    work page 2000

  45. [45]

    Fujisawa, K

    N. Fujisawa, K. Imaizumi, T. Yamagata, Synchronization of dual diffusion flame in co-flow, Experimental Thermal and Fluid Science 110 (2020) 109924

    work page 2020

  46. [46]

    Manoj, S.A

    K. Manoj, S.A. Pawar, S. Dange, S. Mondal, R.I. Sujith, E. Surovyatkina, J. Kurths, Synchronization route to weak chimera in four candle-flame oscillators, Physical Review E 100 (2019) 062204

    work page 2019

  47. [47]

    Pikovsky, M

    A. Pikovsky, M. Rosenblum, J. Kurths, Synchronization: a universal concept in nonlinear science, American Association of Physics Teachers, 2002

    work page 2002

  48. [48]

    Manoj, S.A

    K. Manoj, S.A. Pawar, R.I. Sujith, Experimental evidence of amplitude death and phase-flip bifurcation between in-phase and anti-phase synchronization, Sci. Rep. 8 (2018) 1-7

    work page 2018

  49. [49]

    Katta, W.M

    V.R. Katta, W.M. Roquemore, A. Menon, S.-Y. Lee, R.J. Santoro, T.A. Litzinger, Impact of soot on flame flicker, Proc. Combust. Inst. 32 (2009) 1343-1350

    work page 2009

  50. [50]

    H. Sato, K. Amagai, M. Arai, Flickering frequencies of diffusion flames observed under various gravity fields, Proc. Combust. Inst. 28 (2000) 1981-1987

    work page 2000

  51. [51]

    Fujisawa, Y

    N. Fujisawa, Y. Matsumoto, T. Yamagata, Influence of co-flow on flickering diffusion flame, Flow, Turbulence and Combustion 97 (2016) 931-950

    work page 2016

  52. [52]

    Tamura, G

    Y. Tamura, G. Matsui, Wake-oscillator model of vortex-induced oscillation of circular cylinder, Wind Engineering, Elsevier1980, pp. 1085-1094. [53] A. Hamins, J. Yang, T. Kashiwagi. An experimental investigation of the pulsation frequency of flames. In: editor^editors. Symposium (international) on combustion; 1992: Elsevier. p. 1695-1702

    work page 1992

  53. [53]

    Durox, T

    D. Durox, T. Yuan, F. Baillot, J. Most, Premixed and diffusion flames in a centrifuge, Combust. Flame 102 (1995) 501-511

    work page 1995

  54. [54]

    Fang, J.-w

    J. Fang, J.-w. Wang, J.-f. Guan, Y.-m. Zhang, J.-j. Wang, Momentum-and buoyancy-driven laminar methane diffusion flame shapes and radiation characteristics at sub-atmospheric pressures, Fuel 163 (2016) 295-303

    work page 2016

  55. [55]

    Byram, R.M

    G.M. Byram, R.M. Nelson, The modeling of pulsating fires, Fire Technology 6 (1970) 102-110

    work page 1970